Role of Plasmid Copy Number in the Dynamics of a Single Gene Oscillator

Although understanding all dynamics in the cell may be elusive, we can aim to understand the impact of design choices under our control. We consider a single gene oscillator as a suitable case study to better understand the influence of various parameters on resulting dynamics. With such a simple circuit the number of variables is greatly reduced while maintaining non-trivial dynamics.

As an initial study we consider the effects of repressor choice and plasmid copy number. Here, we create a new single gene oscillator similar to the published lacI oscillator in which lacI represses its own transcription. The repressor we use is the gene treRL, a chimeric repressor with a lacI DNA binding domain and a ligand binding domain that responds to trehalose as an inducer. This slightly modified system produces more regular oscillations than the original lacI oscillator. With a suitable oscillator we investigate the role of plasmid copy number.

Plasmid copy number is an important variable to consider, as plasmids are typical platforms on which synthetic circuits are designed. It is well known that it is difficult to ascertain exact plasmid copy numbers. Furthermore, the copy number varies dynamically with time. However, there are methods to vary relative plasmid copy numbers. Here, we study the influence of gene copy number on the dynamics of the self-repressing single gene oscillator. We compare the treRL oscillator at three different copy numbers: the medium copy origin p15a, the low copy origin psc101, and a single copy integrated into the genome. The reporter is a fast folding fluorescent protein on a separate plasmid with a colE1 origin.

We find that the period and amplitude of oscillations increases as the copy number decreases. Through analysis of a one-dimensional delay differential equation we find that we cannot explain a change in period without changing delays or degradation rates. We also find that the correlation in fluorescence between daughter cells after cell division falls off faster in the oscillator on the p15a origin compared to the psc101 and single copy variants. Similarly, we find that the phase difference between daughter cells grows more rapidly after cell division on the p15a oscillator compared to the psc101 and single copy variants. These results suggest that lower copy number variants of our single gene oscillator lead to more synchronized and regular oscillations.